Preheat your oven to 180°C (350°F). Grease a 22cm (9-inch) round cake pan and line the bottom with parchment paper.
In a medium bowl, sift together the all-purpose flour, baking powder, and salt. Set aside.
In a large mixing bowl, whisk the eggs and granulated sugar together until pale and fluffy, about 3-4 minutes.
Slowly add the extra virgin olive oil to the egg mixture while whisking continuously.
Add the whole milk, fresh lemon juice, lemon zest, and vanilla extract to the wet ingredients and mix until combined.
Gradually fold the dry ingredients into the wet mixture using a spatula until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Once the cake is completely cool, sift the powdered sugar over the top for a light dusting before serving.